Problem: What is the value of the following logarithm? $\log_{196} 14$
Solution: If $b^y = x$ , then $\log_{b} x = y$ Notice that $14$ is the square root of $196$ That is, $\sqrt{196} = 196^{1/2} = 14$ Thus, $\log_{196} 14 = \dfrac{1}{2}$.